Doing Algebra in Grades K-4

1997 ◽  
Vol 3 (6) ◽  
pp. 346-356
Author(s):  
Zolman Usiskin

About thirty-five years ago the movement to incorporate geometry into the elementary grades began. To many elementary school teachers, the mention of the word geometry brought back memories of a high school geometry course that dealt with abstraction and proof. The thought of teaching children this geometry was naturally viewed with incredulity.

1976 ◽  
Vol 23 (3) ◽  
pp. 169-174
Author(s):  
Donald R. Kerr

Elementary school teachers, preservice or inservice, are not usually given the background in geometry that they need. Some college courses for elementary teachers contain no study of geometry. Those courses that do contain geometry may be limited to traditional topics in measurement, some terminology, and certain facts concerning familiar geometric shapes; or they may review the definitions, theorems, and proofs that the teacher has already had in high school. Judging on hearsay, experience, and an analysis of current mathematics texts for teachers, few courses are providing the teacher with what is needed.


1964 ◽  
Vol 57 (6) ◽  
pp. 404-405
Author(s):  
Harry Sitomer

In the spring of 1961, the School Mathematics Study Group convened a group of college mathematicians and high school teachers of mathematics to consider plans for writing an alternate high school geometry course, in which coordinates would be introduced and used as early as feasible.


2009 ◽  
Vol 16 (5) ◽  
pp. 300-307
Author(s):  
Debra Johanning ◽  
William B. Weber ◽  
Christine Heidt ◽  
Marian Pearce ◽  
Karen Horner

Algebra in the early grades (pre-K-2) is a relatively new focus area in the mathematics education community. As students, many of today's elementary school teachers did not study algebra until they were in high school.


1968 ◽  
Vol 15 (5) ◽  
pp. 397-399
Author(s):  
Julius H. Hlavaty

High school teacher of mathematicsand I include myself among them—have long been accustomed to criticisms from colleagues at the college level about the teaching of mathematics in the high schools. Occasionally we have reacted to these criticisms by criticizing our colleagues in the elementary school. Yet yea rs of teaching have convinced me that we all, by and large, do the best we can at all levels. Indeed, I have a profound admiration for the elementary school teachers who, facing very broad responsibi lities, achieve great success in all areas, including mathematics.


2021 ◽  
Vol 11 ◽  
Author(s):  
Ross C. Hollett ◽  
Mark McMahon ◽  
Ronald Monson

To be an effective teacher, a combination of specific professional skills and psychological attributes are required. With increasingly fluid employment conditions, particularly in the international context, recruiters and schools are under considerable pressure to quickly differentiate candidates and make successful placements, which involves more than just determining if a candidate holds an appropriate qualification. Therefore, the aim of this cross-sectional study was to measure theoretically and empirically valuable psychological attributes in an international sample of schoolteachers to determine the most valuable correlates of satisfaction and position duration. An international sample (N = 335) of elementary, middle and high school teachers completed an online survey to capture their workplace satisfaction, position duration and measure 15 psychological attributes using validated instruments. Linear associations were estimated using hierarchical regression with this analysis complemented and compared with follow-up non-linear neural network models. Using regression, lower agreeableness (less people-oriented) emerged as the strongest correlate of longer position duration throughout the cohort. In elementary school teachers, lower impulsivity and higher organizational commitment emerged as the strongest correlates of longer position duration. In high school teachers, better stress tolerance and higher organizational commitment emerged as the strongest correlates of longer position duration. Using neural networks to suggest predictive models, low levels of neuroticism and impulsivity were the strongest predictors of longer position duration in elementary school teachers. High stress tolerance also predicted high work satisfaction in elementary teachers, whereas it was lower impulsivity that most strongly predicted higher work satisfaction in high school teachers. Innovation tendencies, perhaps surprisingly, appeared as a consistent predictor of lower levels of workplace satisfaction across teaching levels. Honesty-humility also emerged as a predictor of shorter position duration, particularly for primary/elementary teachers scoring above the mean. Taken together the results suggest an interesting balancing act that needs to be struck between hiring people-oriented and innovative teachers who may be more effective and adaptable but also at greater risk of changing position, possibly due to an increased interest and ability to transition into new social environments.


1958 ◽  
Vol 5 (2) ◽  
pp. 84-86
Author(s):  
Wilbur Waggoner

ONE NEED NOT READ too widely in the educational literature of today to note a concern for the mathematical capabilities of the persons who are preparing for positions as elementary school arithmetic teachers. “Less than 20 per cent of prospective elementary school teachers understand arithmetic. One study of 211 teachers showed that 150 of them had an abiding hatred for it.” 1 The above quotation appeared in Parade, a magazine written for the lay public. A further discussion on the problem of competency in subject-matter of arithmetic teachers may be found in Problems of Mathematical Education2 published by Educational Testing Service. This report says, “In majority of cases an individual with ambition to teach in an elementary school can matriculate without showing any high school mathematics on his record. He can graduate without studying college mathematics.”


2020 ◽  
Vol 51 (5) ◽  
pp. 600-630
Author(s):  
Inah Ko ◽  
Patricio Herbst

This study proposes task of teaching as an organizer of dimensionality in teachers’ subject matter knowledge for teaching (SMK) and investigates it in the context of measuring SMK for teaching high school geometry (SMK-G). We hypothesize that teachers use different SMK-G in different aspects of their teaching work and that such differences can be scaled and associated with key elements of instruction. Analyses of 602 high school teachers’ responses to two sets of items designed to measure the SMK-G used in two particular tasks of teaching—understanding students’ work (USW) and choosing givens for a problem (CGP)—suggested the two scales of SMK-G to be distinguishable and differently related to experience in teaching high school geometry.


2006 ◽  
Vol 12 (2) ◽  
pp. 100-101
Author(s):  
David Allen

Think back to the geometry you experienced as an elementary school student. Now recall a problem from high school geometry. Often, geometry tasks at the younger grades are limited to identifying shapes or labeling properties; in high school, students are expected to use abstract reasoning to prove a complex relationship. Instruction in geometry has traditionally been overlooked during middle school, which causes a gap between elementary school experiences and the thought processes required in high school.


2004 ◽  
Vol 9 (7) ◽  
pp. 392-397
Author(s):  
Brad Glass

Many of the new elementary sCHOOL and middle school mathematics curricula provide students with opportunities to encounter geometric transformations. Some of the curricula (e.g., MATHThematics, Math Trailblazers, and Investigations in Number, Data, and Space) introduce transformations (such as translations, reflections, and rotations) as motions (slides, flips, and turns) undergone by familiar shapes. How can we make the most of these experiences to ensure that our students are prepared for high school geometry courses? One way is to find out what students understand about transformations and to address any misconceptions they have regarding transformations. In working with eight eighth-grade prealgebra students, I identified one possible misconception as they completed a set of activities using The Geometer's Sketchpad (Jackiw 2001). The students focused on the path followed by a shape, rather than on the relationship between the preimage and image shapes, thereby leading them to incorrect conclusions regarding the equivalency of transformations. The technology-based activities helped some of the students begin to rectify this misconception.


1973 ◽  
Vol 20 (6) ◽  
pp. 457-467
Author(s):  
Marilyn J. Zweng

Mathematics educators generally agree that elementary school teachers should know “something” about geometry. There is little agreement, though, about what that “something” ought to be. If one were to use the textbooks which claim to provide a course in “Geometry for Elementary Teachers” as a guide, we might conclude that the course should be a rehash of the synthetic Euclidean plane geometry of the high school with one chapter on the geometry of the coordinate plane tossed in for flavoring. There arc a couple of notable exceptions to this generalization, but these exceptions, which are in fact quite different from the course described above, do not have an apparent underlying scheme or intent.


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